What's the current in a 10 -mH inductor storing \(50 \mu\) J of energy?

When delving into the concept of how energy is stored in inductors, it's important to understand that an inductor is a passive electronic component which stores energy in its magnetic field as current flows through it. This is similar to how a capacitor stores energy in an electric field.

The energy in an inductor is given by the formula: \[\begin{equation}W = \frac{1}{2}LI^2\end{equation}\]where

• \(W\) is the energy in joules,
• \(L\) is the inductance in henries,
• \(I\) is the current in amperes flowing through the inductor.

The relationship is quadratic, which means that the energy stored increases with the square of the current. Therefore, even a small increase in current can lead to a large increase in the energy stored within the inductor's magnetic field.

Inductance, denoted as \(L\), is a fundamental property of an inductor that quantifies its ability to store magnetic energy. Inductance is determined by the physical characteristics of the inductor, such as the number of turns in the coil, the cross-sectional area of the coil, the coil length, and the type of material the core is made out of.

Factors Affecting Inductance

• The number of turns: More turns means a higher inductance.
• Cross-sectional area: A larger area results in higher inductance.
• Core material: Materials with higher magnetic permeability, such as iron, increase an inductor's inductance.
• Coil length: A shorter coil length often means greater inductance.

It's important for students to grasp these concepts as they significantly affect the behavior of an inductor in a circuit, altering how it interacts with other components and the circuit as a whole.

Understanding the standard units conversion is crucial for solving physics and engineering problems. In the context of our exercise, the initial values were given in millihenries (mH) for inductance and microjoules (µJ) for energy, which are not standard SI units.

To accurately calculate the current, these values needed to be converted to standard units: henries (H) for inductance and joules (J) for energy. This conversion is a matter of applying the appropriate multiplication factor:

• To convert millihenries (mH) to henries (H), we multiply by \(10^{-3}\) because 'milli' signifies a thousandth.
• To convert microjoules (µJ) to joules (J), we multiply by \(10^{-6}\) because 'micro' signifies a millionth.

Learning to convert between units is essential, as it ensures that formulas, which usually require SI units, are applied correctly. This proficiency enables students to tackle a broad range of exercises without confusion over differing unit systems.